chapter 18: data analysis and mining - yale...

Database System Concepts©Silberschatz, Korth and Sudarshan

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Chapter 18: Data Analysis and Mining Chapter 18: Data Analysis and Mining

©Silberschatz, Korth and Sudarshan18.2Database System Concepts - 5th Edition, Aug 26, 2005

Chapter 18: Data Analysis and Mining Chapter 18: Data Analysis and Mining

Decision Support SystemsData Analysis and OLAPData Warehousing Data Mining


Decision Support SystemsDecision Support Systems

Decision-support systems are used to make business decisions, often based on data collected by on-line transaction-processing systems.Examples of business decisions:

What items to stock?What insurance premium to change?To whom to send advertisements?

Examples of data used for making decisionsRetail sales transaction detailsCustomer profiles (income, age, gender, etc.)


DecisionDecision--Support Systems: OverviewSupport Systems: OverviewData analysis tasks are simplified by specialized tools and SQL extensions

Example tasksFor each product category and each region, what were the total sales in the last quarter and how do they compare with the same quarter last yearAs above, for each product category and each customer category

Statistical analysis packages (e.g., : S++) can be interfaced with databases

Statistical analysis is a large field, but not covered hereData mining seeks to discover knowledge automatically in the form of statistical rules and patterns from large databases.A data warehouse archives information gathered from multiple sources, and stores it under a unified schema, at a single site.

Important for large businesses that generate data from multiple divisions, possibly at multiple sitesData may also be purchased externally


Data Analysis and OLAPData Analysis and OLAP

Online Analytical Processing (OLAP)Interactive analysis of data, allowing data to be summarized andviewed in different ways in an online fashion (with negligible delay)

Data that can be modeled as dimension attributes and measure attributes are called multidimensional data.

Measure attributesmeasure some valuecan be aggregated upone.g. the attribute number of the sales relation

Dimension attributesdefine the dimensions on which measure attributes (or aggregates thereof) are viewede.g. the attributes item_name, color, and size of the sales relation


Cross Tabulation of Cross Tabulation of salessales by by itemitem--name name and and colorcolor

The table above is an example of a cross-tabulation (cross-tab), also referred to as a pivot-table.

Values for one of the dimension attributes form the row headersValues for another dimension attribute form the column headersOther dimension attributes are listed on topValues in individual cells are (aggregates of) the values of thedimension attributes that specify the cell.


Relational Representation of CrossRelational Representation of Cross--tabstabs

Cross-tabs can be represented as relations

We use the value all is used to represent aggregatesThe SQL:1999 standard actually uses null values in place of all despite confusion with regular null values


Data CubeData CubeA data cube is a multidimensional generalization of a cross-tabCan have n dimensions; we show 3 below Cross-tabs can be used as views on a data cube


Online Analytical ProcessingOnline Analytical Processing

Pivoting: changing the dimensions used in a cross-tab is called Slicing: creating a cross-tab for fixed values only

Sometimes called dicing, particularly when values for multiple dimensions are fixed.

Rollup: moving from finer-granularity data to a coarser granularity Drill down: The opposite operation - that of moving from coarser-granularity data to finer-granularity data


Hierarchies on DimensionsHierarchies on DimensionsHierarchy on dimension attributes: lets dimensions to be viewed at different levels of detail

E.g. the dimension DateTime can be used to aggregate by hour of day, date, day of week, month, quarter or year


Cross Tabulation With HierarchyCross Tabulation With Hierarchy

Cross-tabs can be easily extended to deal with hierarchiesCan drill down or roll up on a hierarchy


OLAP ImplementationOLAP Implementation

The earliest OLAP systems used multidimensional arrays in memory to store data cubes, and are referred to as multidimensional OLAP (MOLAP) systems.OLAP implementations using only relational database features are called relational OLAP (ROLAP) systemsHybrid systems, which store some summaries in memory and store the base data and other summaries in a relational database, are called hybrid OLAP (HOLAP) systems.


OLAP Implementation (Cont.)OLAP Implementation (Cont.)

Early OLAP systems precomputed all possible aggregates in order to provide online response

Space and time requirements for doing so can be very high2n combinations of group by

It suffices to precompute some aggregates, and compute others on demand from one of the precomputed aggregates

Can compute aggregate on (item-name, color) from an aggregate on (item-name, color, size) – For all but a few “non-decomposable” aggregates such as

median– is cheaper than computing it from scratch

Several optimizations available for computing multiple aggregatesCan compute aggregate on (item-name, color) from an aggregate on (item-name, color, size)Can compute aggregates on (item-name, color, size), (item-name, color) and (item-name) using a single sorting of the base data


Extended Aggregation in SQL:1999Extended Aggregation in SQL:1999The cube operation computes union of group by’s on every subset of the specified attributesE.g. consider the query

select item-name, color, size, sum(number)from salesgroup by cube(item-name, color, size)

This computes the union of eight different groupings of the sales relation:{ (item-name, color, size), (item-name, color),

(item-name, size), (color, size), (item-name), (color), (size), ( ) }

where ( ) denotes an empty group by list.For each grouping, the result contains the null value for attributes not present in the grouping.


Extended Aggregation (Cont.)Extended Aggregation (Cont.)Relational representation of cross-tab that we saw earlier, but with null in place of all, can be computed by

select item-name, color, sum(number)from salesgroup by cube(item-name, color)

The function grouping() can be applied on an attributeReturns 1 if the value is a null value representing all, and returns 0 in all other cases.

select item-name, color, size, sum(number),grouping(item-name) as item-name-flag,grouping(color) as color-flag,grouping(size) as size-flag,

from salesgroup by cube(item-name, color, size)Can use the function decode() in the select clause to replace such nulls by a value such as all

E.g. replace item-name in first query by decode( grouping(item-name), 1, ‘all’, item-name)


Extended Aggregation (Cont.)Extended Aggregation (Cont.)The rollup construct generates union on every prefix of specified list of attributes E.g.

select item-name, color, size, sum(number)from salesgroup by rollup(item-name, color, size)

Generates union of four groupings:{ (item-name, color, size), (item-name, color), (item-name), ( ) }

Rollup can be used to generate aggregates at multiple levels of ahierarchy.E.g., suppose table itemcategory(item-name, category) gives the category of each item. Then

select category, item-name, sum(number)from sales, itemcategorywhere sales.item-name = itemcategory.item-namegroup by rollup(category, item-name)

would give a hierarchical summary by item-name and by category.


Extended Aggregation (Cont.)Extended Aggregation (Cont.)

Multiple rollups and cubes can be used in a single group by clauseEach generates set of group by lists, cross product of sets gives overall set of group by lists

E.g., select item-name, color, size, sum(number)from salesgroup by rollup(item-name), rollup(color, size)

generates the groupings {item-name, ()} X {(color, size), (color), ()}

= { (item-name, color, size), (item-name, color), (item-name), (color, size), (color), ( ) }


RankingRankingRanking is done in conjunction with an order by specification. Given a relation student-marks(student-id, marks) find the rank of each student.select student-id, rank( ) over (order by marks desc) as s-rankfrom student-marksAn extra order by clause is needed to get them in sorted orderselect student-id, rank ( ) over (order by marks desc) as s-rankfrom student-marks order by s-rankRanking may leave gaps: e.g. if 2 students have the same top mark, both have rank 1, and the next rank is 3

dense_rank does not leave gaps, so next dense rank would be 2


Ranking (Cont.)Ranking (Cont.)

Ranking can be done within partition of the data.“Find the rank of students within each section.”select student-id, section,

rank ( ) over (partition by section order by marks desc) as sec-rank

from student-marks, student-sectionwhere student-marks.student-id = student-section.student-idorder by section, sec-rankMultiple rank clauses can occur in a single select clauseRanking is done after applying group by clause/aggregation



Other ranking functions: percent_rank (within partition, if partitioning is done)cume_dist (cumulative distribution)

fraction of tuples with preceding valuesrow_number (non-deterministic in presence of duplicates)

SQL:1999 permits the user to specify nulls first or nulls lastselect student-id,

rank ( ) over (order by marks desc nulls last) as s-rankfrom student-marks



For a given constant n, the ranking the function ntile(n) takes the tuples in each partition in the specified order, and divides them into nbuckets with equal numbers of tuples.E.g.:select threetile, sum(salary)from (

select salary, ntile(3) over (order by salary) as threetilefrom employee) as s

group by threetile


WindowingWindowing

Used to smooth out random variations. E.g.: moving average: “Given sales values for each date, calculate for each date the average of the sales on that day, the previous day, and the next day”Window specification in SQL:

Given relation sales(date, value)select date, sum(value) over

(order by date between rows 1 preceding and 1 following)from sales

Examples of other window specifications:between rows unbounded preceding and currentrows unbounded precedingrange between 10 preceding and current row

All rows with values between current row value –10 to current valuerange interval 10 day preceding

Not including current row


Windowing (Cont.)Windowing (Cont.)

Can do windowing within partitionsE.g. Given a relation transaction (account-number, date-time, value), where value is positive for a deposit and negative for a withdrawal

“Find total balance of each account after each transaction on theaccount”select account-number, date-time,

sum (value ) over(partition by account-number order by date-timerows unbounded preceding)

as balancefrom transactionorder by account-number, date-time


Data WarehousingData Warehousing

Data sources often store only current data, not historical dataCorporate decision making requires a unified view of all organizational data, including historical dataA data warehouse is a repository (archive) of information gathered from multiple sources, stored under a unified schema, at a single site

Greatly simplifies querying, permits study of historical trendsShifts decision support query load away from transaction processing systems


Data WarehousingData Warehousing


Design IssuesDesign Issues

When and how to gather dataSource driven architecture: data sources transmit new information to warehouse, either continuously or periodically (e.g. at night)Destination driven architecture: warehouse periodically requests new information from data sourcesKeeping warehouse exactly synchronized with data sources (e.g. using two-phase commit) is too expensive

Usually OK to have slightly out-of-date data at warehouseData/updates are periodically downloaded form online transaction processing (OLTP) systems.

What schema to useSchema integration


More Warehouse Design IssuesMore Warehouse Design IssuesData cleansing

E.g. correct mistakes in addresses (misspellings, zip code errors)Merge address lists from different sources and purge duplicates

How to propagate updatesWarehouse schema may be a (materialized) view of schema from data sources

What data to summarizeRaw data may be too large to store on-lineAggregate values (totals/subtotals) often sufficeQueries on raw data can often be transformed by query optimizer to use aggregate values


Warehouse SchemasWarehouse Schemas

Dimension values are usually encoded using small integers and mapped to full values via dimension tablesResultant schema is called a star schema

More complicated schema structures Snowflake schema: multiple levels of dimension tablesConstellation: multiple fact tables


Data Warehouse SchemaData Warehouse Schema


Data MiningData MiningData mining is the process of semi-automatically analyzing large databases to find useful patternsPrediction based on past history

Predict if a credit card applicant poses a good credit risk, based on some attributes (income, job type, age, ..) and past historyPredict if a pattern of phone calling card usage is likely to befraudulent

Some examples of prediction mechanisms:Classification

Given a new item whose class is unknown, predict to which class it belongs

Regression formulaeGiven a set of mappings for an unknown function, predict the function result for a new parameter value


Data Mining (Cont.)Data Mining (Cont.)

Descriptive PatternsAssociations

Find books that are often bought by “similar” customers. If a new such customer buys one such book, suggest the others too.

Associations may be used as a first step in detecting causationE.g. association between exposure to chemical X and cancer,

ClustersE.g. typhoid cases were clustered in an area surrounding a contaminated wellDetection of clusters remains important in detecting epidemics


Classification RulesClassification Rules

Classification rules help assign new objects to classes. E.g., given a new automobile insurance applicant, should he or she be classified as low risk, medium risk or high risk?

Classification rules for above example could use a variety of data, such as educational level, salary, age, etc.

∀ person P, P.degree = masters and P.income > 75,000 ⇒ P.credit = excellent

∀ person P, P.degree = bachelors and(P.income ≥ 25,000 and P.income ≤ 75,000)

⇒ P.credit = goodRules are not necessarily exact: there may be some misclassificationsClassification rules can be shown compactly as a decision tree.


Decision TreeDecision Tree


Construction of Decision TreesConstruction of Decision TreesTraining set: a data sample in which the classification is already known.Greedy top down generation of decision trees.

Each internal node of the tree partitions the data into groups based on a partitioning attribute, and a partitioning condition for the nodeLeaf node:

all (or most) of the items at the node belong to the same class,or all attributes have been considered, and no further partitioningis possible.


Best SplitsBest SplitsPick best attributes and conditions on which to partitionThe purity of a set S of training instances can be measured quantitatively in several ways.

Notation: number of classes = k, number of instances = |S|, fraction of instances in class i = pi.

The Gini measure of purity is defined as[

Gini (S) = 1 - ∑

When all instances are in a single class, the Gini value is 0It reaches its maximum (of 1 –1 /k) if each class the same number of instances.

kk

ii-- 11pp22

ii


Best Splits (Cont.)Best Splits (Cont.)Another measure of purity is the entropy measure, which is defined as

entropy (S) = – ∑

When a set S is split into multiple sets Si, I=1, 2, …, r, we can measure the purity of the resultant set of sets as:

purity(S1, S2, ….., Sr) = ∑

The information gain due to particular split of S into Si, i = 1, 2, …., rInformation-gain (S, {S1, S2, …., Sr) = purity(S ) – purity (S1, S2, … Sr)

rr

ii= 1= 1

||SSii||

||SS||purity purity ((SSii))

kk

ii-- 11ppiiloglog2 2 ppii


Best Splits (Cont.)Best Splits (Cont.)

Measure of “cost” of a split: Information-content (S, {S1, S2, ….., Sr})) = – ∑

Information-gain ratio = Information-gain (S, {S1, S2, ……, Sr})Information-content (S, {S1, S2, ….., Sr})

The best split is the one that gives the maximum information gain ratio

loglog22

rr

ii-- 11

||SSii||

||SS||

||SSii||

||SS||


Finding Best SplitsFinding Best Splits

Categorical attributes (with no meaningful order):Multi-way split, one child for each valueBinary split: try all possible breakup of values into two sets, and pick the best

Continuous-valued attributes (can be sorted in a meaningful order)Binary split:

Sort values, try each as a split point– E.g. if values are 1, 10, 15, 25, split at ≤1, ≤ 10, ≤ 15

Pick the value that gives best splitMulti-way split:

A series of binary splits on the same attribute has roughly equivalent effect


DecisionDecision--Tree Construction AlgorithmTree Construction AlgorithmProcedure GrowTree (S )

Partition (S );

Procedure Partition (S)if ( purity (S ) > δp or |S| < δs ) then

return;for each attribute A

evaluate splits on attribute A;Use best split found (across all attributes) to partition

S into S1, S2, …., Sr,for i = 1, 2, ….., r

Partition (Si );


Other Types of ClassifiersOther Types of ClassifiersNeural net classifiers are studied in artificial intelligence and are not covered here Bayesian classifiers use Bayes theorem, which says

p (cj | d ) = p (d | cj ) p (cj ) p ( d )

where p (cj | d ) = probability of instance d being in class cj, p (d | cj ) = probability of generating instance d given class cj,

p (cj ) = probability of occurrence of class cj, and p (d ) = probability of instance d occuring


NaNaïïve Bayesian Classifiersve Bayesian Classifiers

Bayesian classifiers requirecomputation of p (d | cj )precomputation of p (cj )p (d ) can be ignored since it is the same for all classes

To simplify the task, naïve Bayesian classifiers assume attributes have independent distributions, and thereby estimate

p (d | cj) = p (d1 | cj ) * p (d2 | cj ) * ….* (p (dn | cj )Each of the p (di | cj ) can be estimated from a histogram on divalues for each class cj

the histogram is computed from the training instances Histograms on multiple attributes are more expensive to compute and store


RegressionRegression

Regression deals with the prediction of a value, rather than a class. Given values for a set of variables, X1, X2, …, Xn, we wish to predict the value of a variable Y.

One way is to infer coefficients a0, a1, a1, …, an such thatY = a0 + a1 * X1 + a2 * X2 + … + an * Xn

Finding such a linear polynomial is called linear regression. In general, the process of finding a curve that fits the data is also called curve fitting.

The fit may only be approximatebecause of noise in the data, or because the relationship is not exactly a polynomial

Regression aims to find coefficients that give the best possible fit.


Association RulesAssociation Rules

Retail shops are often interested in associations between different items that people buy.

Someone who buys bread is quite likely also to buy milkA person who bought the book Database System Concepts is quite likely also to buy the book Operating System Concepts.

Associations information can be used in several ways. E.g. when a customer buys a particular book, an online shop may suggest associated books.

Association rules:bread ⇒ milk DB-Concepts, OS-Concepts ⇒ Networks

Left hand side: antecedent, right hand side: consequentAn association rule must have an associated population; the population consists of a set of instances

E.g. each transaction (sale) at a shop is an instance, and the set of all transactions is the population


Association Rules (Cont.)Association Rules (Cont.)

Rules have an associated support, as well as an associated confidence. Support is a measure of what fraction of the population satisfies both the antecedent and the consequent of the rule.

E.g. suppose only 0.001 percent of all purchases include milk and screwdrivers. The support for the rule is milk ⇒ screwdrivers is low.

Confidence is a measure of how often the consequent is true when the antecedent is true.

E.g. the rule bread ⇒ milk has a confidence of 80 percent if 80 percent of the purchases that include bread also include milk.


Finding Association RulesFinding Association Rules

We are generally only interested in association rules with reasonably high support (e.g. support of 2% or greater)Naïve algorithm1. Consider all possible sets of relevant items.2. For each set find its support (i.e. count how many transactions

purchase all items in the set).Large itemsets: sets with sufficiently high support

3. Use large itemsets to generate association rules.1. From itemset A generate the rule A - {b } ⇒b for each b ∈ A.

Support of rule = support (A).Confidence of rule = support (A ) / support (A - {b })


Finding SupportFinding Support

Determine support of itemsets via a single pass on set of transactionsLarge itemsets: sets with a high count at the end of the pass

If memory not enough to hold all counts for all itemsets use multiple passes, considering only some itemsets in each pass.Optimization: Once an itemset is eliminated because its count (support) is too small none of its supersets needs to be considered.The a priori technique to find large itemsets:

Pass 1: count support of all sets with just 1 item. Eliminate those items with low supportPass i: candidates: every set of i items such that all its i-1 item subsets are large

Count support of all candidatesStop if there are no candidates


Other Types of AssociationsOther Types of Associations

Basic association rules have several limitationsDeviations from the expected probability are more interesting

E.g. if many people purchase bread, and many people purchase cereal, quite a few would be expected to purchase bothWe are interested in positive as well as negative correlations between sets of items

Positive correlation: co-occurrence is higher than predictedNegative correlation: co-occurrence is lower than predicted

Sequence associations / correlationsE.g. whenever bonds go up, stock prices go down in 2 days

Deviations from temporal patternsE.g. deviation from a steady growthE.g. sales of winter wear go down in summer

Not surprising, part of a known pattern. Look for deviation from value predicted using past patterns


ClusteringClustering

Clustering: Intuitively, finding clusters of points in the given data such that similar points lie in the same clusterCan be formalized using distance metrics in several ways

Group points into k sets (for a given k) such that the average distance of points from the centroid of their assigned group is minimized

Centroid: point defined by taking average of coordinates in each dimension.

Another metric: minimize average distance between every pair of points in a cluster

Has been studied extensively in statistics, but on small data setsData mining systems aim at clustering techniques that can handle very large data setsE.g. the Birch clustering algorithm (more shortly)


Hierarchical ClusteringHierarchical ClusteringExample from biological classification

(the word classification here does not mean a prediction mechanism)

chordata

mammalia reptilia

leopards humans snakes crocodiles

Other examples: Internet directory systems (e.g. Yahoo, more on this later)Agglomerative clustering algorithms

Build small clusters, then cluster small clusters into bigger clusters, and so on

Divisive clustering algorithmsStart with all items in a single cluster, repeatedly refine (break) clusters into smaller ones


Clustering AlgorithmsClustering Algorithms

Clustering algorithms have been designed to handle very large datasetsE.g. the Birch algorithm

Main idea: use an in-memory R-tree to store points that are being clusteredInsert points one at a time into the R-tree, merging a new point with an existing cluster if is less than some δ distance awayIf there are more leaf nodes than fit in memory, merge existing clusters that are close to each otherAt the end of first pass we get a large number of clusters at the leaves of the R-tree

Merge clusters to reduce the number of clusters


Collaborative FilteringCollaborative Filtering

Goal: predict what movies/books/… a person may be interested in, on the basis of

Past preferences of the personOther people with similar past preferencesThe preferences of such people for a new movie/book/…

One approach based on repeated clusteringCluster people on the basis of preferences for moviesThen cluster movies on the basis of being liked by the same clusters of peopleAgain cluster people based on their preferences for (the newly created clusters of) moviesRepeat above till equilibrium

Above problem is an instance of collaborative filtering, where users collaborate in the task of filtering information to find information of interest


Other Types of MiningOther Types of Mining

Text mining: application of data mining to textual documentscluster Web pages to find related pagescluster pages a user has visited to organize their visit historyclassify Web pages automatically into a Web directory

Data visualization systems help users examine large volumes of data and detect patterns visually

Can visually encode large amounts of information on a single screenHumans are very good a detecting visual patterns

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